(2) Assuming that X vehicles need to be sold, the planned profit is 12w yuan.
If the estimated sales volume is 10 and the price is 280,000 units, the rebate for each unit will be 0.5w, and the maximum purchase price for each unit will be 27w. If each unit earns at least 1w, it is 10w', which adds up to 15w, which is greater than 12w, so it can be judged that the planned sales volume is lower than 12w.
The purchase price of X cars =27-(X- 1)*0. 1, the price is 28w, and the rebate is 0.5x
The difference between the sales price and the purchase price is multiplied by the number of vehicles+rebate = 12w.
So there is an equation:
[28-27+(X- 1)* 0. 1]* X+0.5x = 12
x^2+ 14x= 120
x^2+ 14x+49= 169
(x+7)^2= 13^2
X+7= 13 (- 13 is discarded)
x=6